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BUREAU OF MINES 
INFORMATION CIRCULAR/1989 

310 



Bureau of Mines Geotechnical 
Centrifuge Research-A Review 

By Paul C. McWilliams 



UNITED STATES DEPARTMENT OF THE INTERIOR 



Mission: Asthe Nation's principal conservation 
agency, the Department of the Interior has respon- 
sibility for most of our nationally-owned public 
lands and natural and cultural resources. This 
includes fostering wise use of our land and water 
resources, protecting our fish and wildlife, pre- 
serving the environmental and cultural values of 
our national parks and historical places, and pro- 
viding for the enjoyment of life through outdoor 
recreation. The Department assesses our energy 
and mineral resources and works to assure that 
their development is in the best interests of all 
our people. The Department also promotes the 
goals of the Take Pride in America campaign by 
encouraging stewardship and citizen responsibil- 
ity forthe public lands and promoting citizen par- 
ticipation in their care. The Department also has 
a major responsibility for American Indian reser- 
vation communities and for people who live in 
Island Territories under U.S. Administration. 



( jjvJM &&* \ BjAfitMi tf / hh^d 



Information Circular 9218 

n 




Bureau of Mines Geotechnical 
Centrifuge Research-A Review 

By Paul C. McWilliams 



UNITED STATES DEPARTMENT OF THE INTERIOR 
Manuel J. Lujan, Jr., Secretary 

BUREAU OF MINES 
T S Ary, Director 







Library of Congress Cataloging in Publication Data: 




McWilliams, P. C. (Paul C.) 

Bureau of Mines geotechnical centrifuge research— a review. 

Bureau of Mines information circular; 9218) 

Bibliography: p. 19. 

Supt. of Docs, no.: I 28.27:9218. 

1. Tailings embankmemts— Testing. 2. Rock mechanics. 3. Centrifugation. I. Ti- 
tle. II. Series: Information circular (United States. Bureau of Mines); 9218. 



TN295.U4 



[TN288] 



622 s [622'.7] 



88-607916 



CONTENTS 

Page 

Abstract 1 

Introduction 2 

Acknowledgment 2 

Brief history of geotechnical centrifuge testing 2 

Rock mechanics testing 2 

Soil mechanics testing 3 

Current status, geotechnical centrifuging in United States I 4 

Centrifuge and model testing 5 

Similitude, scaling, and modeling-of-models 5 

Bureau of Mines sponsored geotechnical centrifuge projects 6 

First experimental series-University of Cambridge- 1977 6 

Experimental goal and design 6 

Test equipment 6 

Experimental results 7 

Second experimental series-Univefsity of Cambridge-1978 9 

Experimental goal and design 9 

Experimental results 10 

First experimental series-Sandia National Laboratories-1981 11 

Experimental goal and design 11 

Test equipment 12 

Experimental results 12 

Second experimental series-Sandia National Laboratories- 1983 15 

Experimental goal and design 15 

Test equipment 15 

Experimental results 15 

Other Bureau of Mines projects 17 

Grain-size mapping between prototypes and centrifuge models 17 

Centrifuge usage to solve rock mechanics problems 17 

Conclusions 18 

References 19 

ILLUSTRATIONS 

1. University of Cambridge's 13-ft radius centrifuge 7 

2. Cambridge experiment-embankment prior to testing 8 

3. Cambridge experiment-embankment after testing 9 

4. Sandia National Laboratories' 25-ft radius centrifuge 11 

5. Sandia experiment-embankment prior to testing 13 

6. Sandia experiment-embankment after testing 14 

7. Sandia's first experimental series-steady-state phreatic surface at 90-g, 125-g, and 150-g scaling 14 

8. Sandia's second experimental series-equipotential contours 16 



UNIT OF MEASURE ABBREVIATIONS USED IN THIS REPORT 


ft foot m 


meter 


h hour min 


minute 


in inch pet 


percent 


lb pound st 


short ton 


lb/st pound per short ton yr 


year 



BUREAU OF MINES GEOTECHNICAL CENTRIFUGE 
RESEARCH-A REVIEW 

By Paul C. McWilliams 1 



ABSTRACT 

The U.S. Bureau of Mines has, primarily through its contract program, used large-scale centrifuges 
to determine design criteria for tailings embankments. The centrifuge runs were made at two instal- 
lations, the University of Cambridge, Cambridge, England and Sandia National Laboratories, Albuquer- 
que, NM. The major problems considered were as follows: slope stability of embankments, modeling 
erosion and seepage, use of the phreatic surface level to ascertain the validity of centrifuge modeling, 
and the effects of compaction and weathering on a tailings embankment. This report summarizes the 
results of the four test series conducted at University of Cambridge and Sandia National Laboratories. 
A review of prior centrifuge applications to mining problems is included. Consideration is given to 
future centrifuge application to mining problems in both soil and rock mechanics. 



Mathematical statistician, Spokane Research Center, U.S. Bureau of Mines, Spokane, WA. 



INTRODUCTION 



The prime motivation for writing this report is to pre- 
sent-in digest form-recent centrifuge work done relative 
to the safety of mine tailings embankments. It is hoped 
that this review will motivate the reader to consider the 
detailed reports themselves. These reports written at the 
University of Cambridge (10-11), 2 U.S. Army Waterways 
Experimental Station Vicksburg, MS, (40), and Sandia 
National Laboratories (37-38), detail the four major 
experimental tests. 



The Bureau of Mines has now been involved in centri- 
fuge testing in rock and soils mechanics for about 40 yr. 
Of particular interest is the 10 yr series of centrifuge ex- 
periments conducted by Panek (21-26) at College Park, 
MD, from 1952 to 1961. Panek's area of interest was to 
consider the effects of rock bolts on underground mine 
roofs. More detail on Panek's work is presented in the 
section on "Rock Mechanics Testing." 



ACKNOWLEDGMENT 



The author wishes to thank Bill Stewart, mining en- 
gineer, Bureau of Mines, Spokane, WA, who was the 
original project leader on the coal waste embankment 



centrifuge work done at the University of Cambridge in 
1977 and 1978. 



BRIEF HISTORY OF GEOTECHNICAL CENTRIFUGE TESTING 



ROCK MECHANICS TESTING 

Many authors (1, 6-7, 32) have chronicled accounts of 
the use of centrifuge testing in geotechnical investigations. 
Of particular interest to this Bureau of Mines report are 
those works that apply to the mining industry. The most 
prominent pioneer in the use of centrifuge testing in rock 
mechanics is Bucky (3), who initiated such experimentation 
in this country at University of Columbia, New York, NY 
in 1931. Bucky studied model beams of various materials 
by increasing their self weight while rotating at increasing 
speeds in the centrifuge. It was concluded that: 

"If in the model the pull of gravity on each part 
can be increased in the same proportion as the linear 
scale is decreased, then the unit stress at similar 
points in the model and the prototype will be the 
same, and the displacement or deflection of any 
point in the model will represent to scale the 
displacement of the corresponding point in the 
prototype (3)." 

Bucky published several articles with mining applica- 
tions from 1931 to 1949. The first work for the Bureau 
in centrifuging was by Wright (43) in 1948. The objective 
of this work was to determine optimal pillar placements 
that would provide a safe working environment. For this 
purpose, a set of charts was produced from the centrifuge 
modeling simulations. 

Italic numbers in parentheses refer to items in the list of references 
at the end of this report. 



The next notable works of this kind were conducted by 
Panek of the Bureau. An extensive series of tests was 
conducted in which models of layered, bolted roof beams 
were tested, resulting in several publications (21-26) over 
a 10-yr period. Panek's centrifuge work respresented a 
marked improvement over earlier designs, with strain 
gages being incorporatd for the first time. (To give the 
reader perspective of the state of the art in centrifuge 
modeling in 1952, Panek's centrifuge could carry a 90-lb 
payload at up to 2,600 gravity (g). The machine had a 
radius of 2 ft.) Of particular interest was the fact that 
Panek's work involved nondestructive testing. In a 
majority of other investigations, centrifuge testing was 
continued until failure occurred, thus Panek's work was 
novel from this point of view. 

Some more detail about Panek's work seems appro- 
priate. Panek enumerated six advantages to centrifuge 
testing: 

1. The model can be made of a material different from 
that of the prototype (for experimental convenience, lime- 
stone was used as the test material). 

2. The model need not be tested to destructive, hence 
variations in strength or other properties from one test 
specimen to another are not reflected in the results. 

3. The effects of changes in one or more variables can 
be studied by performing a series of tests on a single 
model. 

4. The state of strain in the test model can be 
determined. 



5. By measuring the model strains corresponding to 
several load values a load-strain relation can be deter- 
mined from a single test. 

6. The test results, which consist of quantitative 
relations between the load, the strain, and the dimensions 
and properties of the structural members, are directly 
applicable to any prototype that satisfies the simularity 
requirements, irrespective of its dimensions or component 
materials. 

Panek proceeded to show that for rockbolting problems, 
the laws of similitude 3 could be relaxed for the material 
properties of the bolt itself. Further, since plane-strain 
was used to model the action of the roof, one could also 
relax the similitude criteria for equality of Poisson's ratio 
between model and prototype. These arguments are de- 
tailed in the report "Theory of Model Testing as Applied 
to Roof Bolting" (22). In the last series of tests (23-26), 
Panek was concerned with modeling bolted bedded mine 
roofs. It was concluded that centrifuge results are con- 
sistent with theoretical calculations. Methodology of how 
to best space rockbolts is discussed (23-24). Panek consid- 
ered the problems of separated roof bedding-the suspen- 
sion problem-and the effect that friction between the beds 
has on this problem (25-26). Here one sees the researcher 
observing the mechanism of the action and reaction 
through centrifuge experimentation. 

At about the same time, Caudle (5) was also working 
with supported beam theory problems. In a later publi- 
cation, Clark (7) stated that: "A unique and vital charac- 
teristic of the centrifugal testing of beams and other struc- 
tures which has not been explored is the determination of 
the behavior of a beam after initial fracture takes place, 
and the stress can no longer be determined analytically. 
That is, after initial fracture has taken place, further defor- 
mation and failure due to body forces can be created and 
effects observed only in a centrifuge." Obviously Clark 
feels that, given a proper centrifuge for the situation, sig- 
nificant advances in the measuring of post-failure defor- 
mations can be made only through centrifuge work. 

In 1965, Hoek published an article "The Design of a 
Centrifuge for the Simulation of Gravitational Force Fields 
in Mine Models" (13). In this article the author discusses 
the 4-1/2-ft radius 1,000-g centrifuge designed and con- 
structed by the South African Council for Scientific and 
Industrial Research, Pretoria, South Africa. This machine 
was used for photoelastic stress determinations (at 100 g) 
and brittle fracture studies (at 600 g). Hoek like Clark (7), 
holds that a 2,000-g machine is desirable for future hard 
rock centrifuge work. 

Ramberg did extensive work in using the centrifuge to 
study domes, folds, gravity sliding, extrusion of lava, etc. 
This work was started by Ramberg at the University of 
Chicago, Chicago, IL in 1960 and was later switched to the 
Uppsala Centrifuge Laboratory in Uppsala, Sweden. In 
the test "Gravity, Deformation, and the Earth's Crust" (30), 

3 See section, "Similitude, Scaling, and Modeling-of-Models." 



Ramberg stated: "The principle of centrifuged dynamic 
models is simply that the centrifugal force plays the same 
role in the models as does the force of gravity in geological 
structures. However, since the centrifugal force per unit 
mass, which in magnitude equals the centripetal acceler- 
ation, but is oppositely directed, may be made several 
thousand times stronger than the gravitational force per 
unit mass, model materials can be used that are several 
thousand times stronger and correspondingly more viscous 
than materials usable in noncentrifuged models of the 
same size." Thus, another centrifuge innovator states the 
advantage of using the centrifuge in lieu of other modeling. 
In the early 1980's, Sutherland of Sandia National Labo- 
ratories (34-36) conducted a series of subsidence tests on 
their 25-ft centrifuge. This machine— using a swing plat- 
form to position the model-is capable of carrying a pay- 
load of over 1,000 lb and attaining over 150-g acceleration. 
Use of this large-scale machine represents another mile- 
stone in centrifuge applications in this country; previously 
only smaller machines were available for geotechnical use 
here. Sutherland and associates developed finite-element 
computer models and discrete-element models for the rock 
rubble flow in a mine opening resulting from subsiding 
overburden ground. The centrifuge results were then com- 
pared with the analytic model calculations. Agreement 
between the centrifuge tests, the finite-element models, 
and the discrete-element models was quite good. 

SOIL MECHANICS TESTING 

Almost all the early soil mechanics centrifuge work was 
focused in the Soviet Union (1930's) and other European 
locations (1960's). In the mid-1930's, Pokrovsky and asso- 
ciates published articles concerned with modeling and cen- 
trifuge applications to problems in soil mechanics (27-28). 
Later Malushitsky (19) published a book on centrifuge 
model testing relative to slope stability in embankments. 
During the 1970's, several prominent European and Amer- 
ican soil mechanic engineers visited the Soviet Union 
installations. In mining, the Soviet Union is very reliant on 
centrifuge testing in designing and establishing slope sta- 
bility criteria for actual prototype waste disposal sites. 
The Soviet Union also used the centrifuge to "directly 
model" a variety of other geotechnical problems (29). This 
approach is in contrast to that of U.S. designers who rely 
primarily on computer models and calculation techniques 
to establish prototype design criteria. Malushitsky's book 
is effectively a user's guide for designing embankments on 
a geotechnical centrifuge. 

Beginning in the early 1960's, European usage of centri- 
fuges to study soil mechanics application became common 
practice. However, most of these early centrifuge appli- 
cations were not related to mining problems. The majority 
of the work was done in Sweden and England. Professors 
Roscoe and Schofield of the Engineering Department at 
the University of Cambridge became prominent practi- 
tioners of centrifuge soil mechanics work in the late 1960's. 



Many of the current centrifuge-oriented engineers in the 
United States studied at the University of Cambridge dur- 
ing the 1970's. 

The work discussed hereafter was done in the last 15 yr. 
One of the centrifuge applications in mining was funded by 
the Bureau, with the work being done at the University of 
Cambridge in 1977 (10-11). Waterways Experimental 
Station, U.S. Corp. of Engineers, Vicksburg, MS, was also 
involved as the primary contractor (40). The objective of 
these government funded studies was to establish design 
criteria for slope stability of coal waste embankments. 
Motivation for the slope stability question was due to the 
1972 Buffalo Creek disaster in West Virginia when a coal 
refuge retaining dam failed, killing 116 people. The Bu- 
reau's centrifuge work was continued at Sandia National 
Laboratories by Sutherland in the early 1980's (37-38). 
These projects are described in detail in this report. 

There was other centrifuge work in soils that is of 
interest to the mining industry. The University of Florida, 
Gainesville, FL, has studied problems in evaluating the 
sedimentation and consolidation characteristics of 
phosphatic waste clays (2, 18). The Japanese, Scott at 
California Institute of Technology, Pasadena, CA, and Ko 
at the University of Colorado, Boulder, CO have addressed 
problems involving underground tunnel construction. Ko 
has also investigated many other topics; of particular 
interest is that of cone penetrometers, slope stability of 
embankments, and overtopping earth dams (9, 14-15). 
Goodings of the University of Maryland, College Park, 
MD (12) has work relative to erosion and seepage 
modeling in a tailings embankment. This work is 
derivative from the aforementioned work in embankments 
by Schofield and Goodings at the University of Cambridge 
(10-11). In addition, Goodings is currently doing research 
on reinforced soil walls and particle scale effect in 
modeling slope stability. 

Certainly, there are other works in soil and rock 
mechanics not discussed herein. Although not a mining 
problem per se, the work of Schmidt and Holsapple at 
Boeing Co., Seattle, WA is held in high esteem. They use 
centrifuge testing to simulate the effects of cratering. An 
example problem would be to predict the resulting crater 
size formed from the detonation of a high-explosive device. 
Some 40 publications by Schmidt and/or Holsapple are 
enumerated in Cheney's biography of centrifuge paper (6, 
pp. 10-22). To paraphrase Cheney's appraisal of this work 
(6, p. 2): 

"The work of Schmidt and Holsapple has revolu- 
tionized the science of crater prediction at nuclear 
explosive levels and was accomplished by a scale test 
at Boeing Co. in Seattle, WA, using small chemical 
explosives and impact of small projectiles at high 



velocities. The results dramatically reduce the size 
estimates for craters formed by near-surface large- 
yield nuclear explosives and by planetary impact of 
large bodies." In a recent experiment (6, p. 256), 
Schmidt and Holsapple were able to model a 40-ton 4 
explosive event of their centrifuge. The authors state 
that: "The results were gratifying. In contrast to the 
"state-of-the-art" numerical prediction, which proved 
to be in error by over 100 pet in volume of the 
crater, the single-shot centrifuge prediction was 
accurate to within 12 pet. Subsequent refinement of 
the model gave even better accuracy." 

From the preceding discussion of the history of geo- 
technical centrifuge applications, it would seem justifiable 
to conclude that these are exciting times for centrifuge 
users in the areas of soils and rock mechanics. 

CURRENT STATUS, GEOTECHNICAL 

CENTRIFUGING IN 

UNITED STATES 

Currently there is considerable momentum towards 
geotechnical usage of centrifuges in this country. Cheney 
(6) has printed an extensive bibliography of centrifuge 
publications. There were 37 publications listed between 
1931 to 1977, but in 1983 alone there were 32 publications. 
If the number of publications represents some measure of 
growth, then one can conclude that the amount of geotech- 
nical centrifuge work is increasing at an almost exponential 
rate. Three large-scale geotechnical centrifuges are avail- 
able in this country-at Sandia National Laboratories, at 
the University of California at Davis, and at the University 
of Colorado. In addition, there are several smaller instal- 
lations being used: again at Davis and Colorado, Cali- 
fornia Institute of Technology, University of Maryland, 
University of Princeton, Princeton, NJ, University of Ken- 
tucky, Lexington, KY, Boeing Co., Massachusetts Institute 
of Technology, Cambridge, MA, New Jersey Institute of 
Technology, Newark, NJ, Ohio State University, Colum- 
bus, OH, and University of Florida. This list is by no 
means complete; there may be other academic and com- 
mercial installations that are not included herein. Several 
centrifuge users, notably Scott at California Institute of 
Technology (8, 33), Schofield (31) at University of Cam- 
bridge, Ko at the University of Colorado, and Kutter (16) 
now at the University of California, Davis, have incorpo- 
rated dynamic effects into their centrifuge modeling. Sim- 
ulation of earthquakes and other ground movement is now 
incorporated into current centrifuge testing. 

4 In this report, "ton" indicates 2,000 lbf. 



CENTRIFUGE AND MODEL TESTING 



A very logical question that might be asked is: why is 
it necessary to use a centrifuge for model testing? Tradi- 
tionally, laboratory scientists conduct a small-scale exper- 
iment of some kind prior to large-scale involvement. In 
more recent times, mathematical models are often substi- 
tuted for (or are complementary to) laboratory scale mod- 
els. Certainly centrifuges are not commonplace instru- 
ments in most laboratories. Further, the cost in both 
money and time for running centrifuge experiments is not 
cheap. Thus, argumentation must be provided to justify 
using a centrifuge to model prototype situation. 

Proponents of centrifuge usage (6-7, 32) provide a vari- 
ety of reasons why a centrifuge is a very good modeling 
tool. The following is a synopsis of some of their major 
ideas: 

1. One can directly model prototype situations. Par- 
ticularly in soils, the same material can be used in the 
model as exists in the prototype. In many cases, a centri- 
fuge model better satisfies the laws of similitude between 
model and prototype than does the corresponding 1-g 
model. 5 For example, since the stress field functions 
exactly the same on the centrifuge and the prototype, 
gravity load situations can be simulated easily on the 
centrifuge (assuming identical friction, cohesion, and den- 
sity properties exists between the model and prototype (40, 



p. 14)). Further, time-sequenced events can be forecasted 
on the centrifuge; a decided advantage over most 1-g 
models. 

2. Sophisticated computer models can be verified via 
centrifuge experimentation. Many centrifuge advocates 
consider this to be the prime use of their experimentation. 

3. It can be used as an educational aid. Insight as to 
the mechanism of failure is often cited as a reason for cen- 
trifuge testing. Visually seeing how a structure reacts to 
various loading conditions without actual failure is also 
quite useful. 

4. Tests can be replication of testing. Often laboratory 
models are destroyed during testing, and are thus, one shot 
by nature. In contrast, many centrifuge models can be 
constructed within a reasonable time span. For example, 
a centrifuge model of a tailings embankment may be con- 
structed in 2-3 h and a complete parameter study of a 
problem could be conducted in a few days. There are, of 
course, centrifuge modeling problems that do require time 
and care in preparation, particularly those in rock mechan- 
ics. Nonetheless, replication of testing via centrifuge mod- 
eling is very important, yet advocates of centrifuge use 
often fail to adequately emphasize this point. Although 
the preceding list is not exhaustive, it does give some indi- 
cations why modelers are turning to the centrifuge more 
frequently than before. 



SIMILITUDE, SCALING, AND MODELING-OF-MODELS 



For any small-scale model to be representative of a 
corresponding prototype situation, the model ideally should 
possess all the important characteristics of the prototype. 
In the book, "Dimensional Analysis and Theory of Models" 
(17), Langhaar differentiates between desirable kinds of 
similarity. Geometric similarity is usually easiest to obtain; 
in a centrifuge, geometric dimensions scale in proportion 
to the number of gravities (N) transmitted to the model. 
Kinetic and dynamic similarities are also desirable. As 
stated previously, one of the chief advantages of using a 
centrifuge is that the stress fields in is exact correspon- 
dence between the model and the prototype. However, 
many other pertinent variables have laws of correspon- 
dence of their own. For example, in soil applications on 
a centrifuge, time scales as follows: proportionate to N in 
dynamic terms, proportionate to N 2 inthe case of diffusion, 
and identically scaled in the case of viscous flow (40, 
p. 15). 

Ideally, one would strive for complete similarity, in 
which all the variables of interest would scale in the same 



1-g modeling refers to doing the work under influence of the 
earth's gravity, i.e., normal laboratory modeling. 



manner. Practical considerations may require the modeler 
to be less stringent, relaxing similarity requisites on vari- 
ables of lesser importance. The previous referenced work 
of Panek (22-26) shows the skill of the researcher in being 
able to relax some relatively unimportant similarity 
requirements in order to proceed with the research. 

There are two approaches taken by centrifuge users in 
evolving the laws of similitude: 

1. Scaling relationships are derived using the basic laws 
of physics. Two basic "truisms" are predicated; namely 
that the centrifuge's acceleration is N times that of the 
prototype and that the physical dimensions of the 
prototype are N times those of the centrifuge model. 
Given those as a basis, one can derive relationships 
between prototype and the centrifuge's stresses, time 
relationships, erosion equations, capillary rise, etc. 

2. Dimensional analysis provides another approach to 
the problem. Here similitude relationships evolved by 
establishing dimensionless products involving pertinent 
parameters of the scientific phenomena being investigated. 
Again, the tenets involving accelerations and physical 
dimensions are involved in evolving the resulting similitude 
statements. This approach uses Buckingham's Pi theorem, 



which states: "If an equation is dimensionallly homogen- 
eous, it can be reduced to a relationship among a complete 
set of dimensionless products." 

A noteworthy consideration in soil work is that centri- 
fuge models are often more favorable in terms of similarity 
than are 1-g models. Using dimensional analysis, Overson 
(6) derives six important variable relationships needed to 
model the settling of footings on a dry sand surface. Con- 
ventional (1-g) modeling is compared with centrifuge mod- 
eling. Of the six relationships, the conventional modeling 
preserves similarity in two of the relationships, while the 
centrifuge modeling preserves similarity in five of the rela- 
tionships. Hence, the modeler chose to use the centrifuge 
for the work. 

The scaling process is both interesting and complex, 
and therefore deserves more detailed consideration than 
provided herein. An article by Cargill (4) is recommended 



for a straightforward look at scaling centrifuge modeling of 
transient waterflow. 

The preceding is a very brief sketch of the topic of 
similitude. To comply with the intent of this paper, con- 
sideration was restricted to comparisons between the cen- 
trifuge and the prototype. Thus, centrifuge similitude 
represents a subset of the general topic, and the interested 
reader is invited to consider more detailed explanations as 
found in the books of Langhaar (17) and Ramberg (30). 

Another concept of importance is the so-called mod- 
eling-of-models. Cargill (4) provides this definition: "To 
test the scaling laws which relate prototype and its centri- 
fuge model, a series of reduced scale models can be tested 
at the necessary increased gravity ratios so that they all 
represent the same hypothetical prototype." This tech- 
nique is often used as a first step when introducing a new 
problem to the centrifuge. 



BUREAU OF MINES SPONSORED GEOTECHNICAL CENTRIFUGE PROJECTS 



The following is an attempt to put into summary form 
the results of the contract program which the Bureau has 
funded in centrifuge research. Five detailed reports have 
been previously published: three on the Cambridge work 
(10-11, 40), and two on the Sandia work (37-38). All of 
this work was done for the Bureau during the years 1977 
to 1984. Coal waste was chosen as the material of interest. 
This was quite logical at the time, for there had been two 
recent disastrous coal waste failures, one at Buffalo Creek, 
WV, and another at Aberfan, Wales. Coal waste material 
is hard to work with as a modeling material. The basic 
problem encountered was the difficulty in making the 
sample representative of the prototype while still adhering 
to grain-size reduction demands of centrifuge testing. 



Deterioration of coal waste fines with time was an addi- 
tional problem. 

Since it was deemed prudent to use a reasonably large- 
scale model, the geotechnical centrifuge at the University 
of Cambridge was selected for use on our first project in 
1977. At that time, use of the large-scale Cambridge 
machine (13-ft working radius) was the most logical op- 
tion. The U.S. Army Waterways Experimental Station 
(Townsend) 6 was the prime contractor, subcontracting the 
actual centrifuge runs to Cambridge (Goodings, Scho- 
field). 6 After 1980, Sandia National Laboratories (Suther- 
land) 6 made its 25-ft-radius machine available to the Bu- 
reau on a governmental interagency basis. Since 1980, all 
of the Bureau's centrifuge work was done at Sandia. 



FIRST EXPERIMENTAL SERIES-UNIVERSITY OF CAMBRIDGE-1977 



EXPERIMENTAL GOAL AND DESIGN 



TEST EQUIPMENT 



Since this series of mine waste embankment tests as 
the first of its kind in the Western world, this was truly 
an orientation set of experiments. Slope stability analysis 
was of first order of interest. As the test series contin- 
ued, emphasis switched to consideration of erosion and 
seepage problems. In this series, 13 experimental tests 
were conducted. 



The University of Cambridge's geotechnical centrifuge 
(fig. 1) has a working radius of 13 ft from the center of the 
rotor to the mid-depth of the soil in a model on the swing- 
ing platform. The soil is enclosed in a strong box. The 
centrifuge was capable of attaining 150 g. The maximum 

Principal investigators. 




Figure 1 .—University of Cambridge's 13-ft radius centrifuge. 



weight (both soil and strong box) that can be carried is 
slightly over 400 lb. Transducers are available to monitor 
displacements in the embankment. A system that allows 
the flow of water through the embankment is aboard. 
Manometers were used to measure phreatic height. Via 
a mirror system, video pictures documented the centrifuge 
runs. Instant still photography was also available. 

EXPERIMENTAL RESULTS 

Two reports (10, 40) detail results of this experimental 
series. A few highlights of these reports are of interest 
here. The material used was coal waste taken from an 
embankment in the southwest United States. Figure 2 
illustrates a typical centrifuge model embankment prior to 



testing. To make the modeling realistic with prototype 
situations, flow of water through the embankment soil is 
a requisite. There are problems and ensuing constraints 
imposed on the experiment due to accommodating water- 
flow. The laws of similitude were examined to determine 
proper model scaling. It was necessary to make adjust- 
ments in the coal waste material's particle size distribu- 
tions for two reasons: 

1. Very large particles were eliminated to 
accommodate the small size of the centrifuge models 
(typically 10 in high, 30 in long, 6 in deep). 

2. Permeabilities had to be adjusted to accommodate 
the waterflow problems (11, pp. 27-31). 




Figure 2.— Cambridge experiment— embankment prior to testing. 



By running the centrifuge at high accelerations, slope 
failures were induced. Undesirable seepage conditions, 
which caused failures at the embankment's toe, were reme- 
died by using coarse waste at the toe as is done in many 
southwestern tailings embankments. Figure 2 is a model 
embankment prior to running, while figure 3 is a post-run 
view of a failed embankment. Note the classic slip circle 
failure situation here. The final runs of this series of 
experiments were concerned with the seepage-erosion 
problem which is the focus of the next Cambridge series. 

Major conclusions from this experiment were as follows: 

1. The experimental nuances of modeling coal waste 
were solvable, and a 100-ft prototype could be modeled. 
These experiments indicated that compaction of material 
is not required for modeling. 

2. The tested material was highly susceptible to both 
surface erosion and seepage failure problems. There are 
both modeling and real-world difficulties in this regard; in 



this and the next test series the authors address both of 
these problems. 

3. Centrifuge modeling techniques are adaptable and 
flexible for coal waste embankments. 

In addition to the preceding, there are other points of 
consideration: 

1. The research was new in that the previous Soviet 
work of Malushitsky (19) in 1975 was of different grain 
size and focused on the rate-of-construction failures. 

2. The embankments behaved (except in one case 
which, unfortunately, was in sharp divergence) as predicted 
in regard to slope stability calculations. 

3. The addition of toe-drains improved mass slope 
stability greatly. Also, sealing the upstream face with a 
slurry of low permeability improved the stability of the 
downstream face. However, inclusion of an undrained, but 
a highly permeable soil key was found to reduce 
embankment stability. 







Figure 3.-Cambridge experiment-embankment after testing. 



4. Both the finite-element phreatic surface and the 
factor of safety calculation methods matched nicely with 
the test results in the runs. 

Major problems encountered in this experiment were as 
follows: 

1. A practical problem was how to provide and control 
sufficient water to the model. 



2. There was, in fact, no real prototype to scale to. 
Size limitations of the centrifuge box was a problem in 
constructing models of prototypical heights. 

3. Trying to reconsile the divergence between seepage- 
erosion effects were primary motivators in having a second 
Cambridge test. 



SECOND EXPERIMENTAL SERIES-UNIVERSITY OF CAMBRIDGE-1978 



EXPERIMENTAL GOAL AND DESIGN 

"The objective of the investigations in this research was 
basically modeling of models; it set out to examine effects 
on model behavior due to the changes in model scale and 
particle size distributions, with special attention given 
to changes in slope stability, permeability, and rate of embankment up. 



retrogression" (ll). 7 Six experimental models were tested 
in this series. The experimental setup for this series of 
tests was effectively the same as described for the first 



7 Rate of retrogression refers to embankment failures induced by 
successive slides of the downstream face emitting from the toe of the 



10 



series. Many complex problems were addressed, including 
the effects of compaction and the modeling of seepage- 
erosion effects. 

EXPERIMENTAL RESULTS 

Two reports (11, 40) describe this experimental series 
in detail. Owing primarily to permeability considerations 
(also owing to the physical size of the sample container), 
particle size adjustments were required for this analysis. 
In deriving the scaling laws for waterflow, Darcy's law (11, 
p. 3) gives as the velocity of flow in the centrifuge: 



= kNi 



(1) 



where v = flow velocity, 

k = permeability, 

i = hydraulic gradient, 

and N = number of gravities. 

This scaling law is significant in that the waterflow in 
the model is quite rapid, being in proportion to the accel- 
eration of the centrifuge. Therefore, providing an ade- 
quate amount of water for the centrifuge is a practical 
concern. Slip circle analysis was again applied to all model 
runs. 

While scaled down particle size did not effect the stress 
relationships between model and a hypothetical prototype, 
such scaling is very important in establishing laws of 
similitude regarding permeability. 

The permeability relationship between model and pro- 
totype reduces to the following effective particle size 
relationship (11, p. 13): 



D 



io. 



= D 



■*' 



(2) 



where 



D, 



10% cumulative distribution point from 
the model, 8 



and 



D 10 = 10% cumulative distribution point from 
p the prototype, 

N = number of gravities centrifuge attains. 



D is the diameter of the soil particles. D 10 indicates that 10% of 
the soil sample is of this diameter or less, D^ indicates that 50% of the 
soil is of this diameter or less. 



The experiments found a conflict between the above 
results and that obtained when modeling surface erosion. 
The appropriate scaling law for erosion is (12, p. 152): 



D 



50 r , 



= D 



50 p / N 



(3) 



where D^ = 50% cumulative distribution points. 

Since equations 2 and 3 cannot both be satisfied for var- 
ious values of "N", this demonstrates that one cannot con- 
currently model seepage and erosion effects simultaneously 
on the centrifuge. 

Major experimental results were as follows: 

1. The particle size problems that evolved during the 
modeling-necessitating parameter changes as required- 
negated the modeling-of-models effort. 

2. One can model either mass instability (induced by 
waterflow through the embankment) or surface erosion 
effects separately. Since different particle size alterations 
are requisite for each of these efforts, it is not possible to 
concurrently model both of these effects. 

3. The critical type of failure is very dependent on the 
permeability of the material. For low permeability situa- 
tions, rate of embankment constructions may be a critical 
parameter. Intermediate permeability provides potential 
slope stability failure because of pore pressures resulting 
from the throughflow. Finally, high permeability present 
problems in regard to erosion effects. 

4. Compaction of material in lifts may aggravate the 
tendency for erosion problems so that the possible bene- 
ficial effects on mass slope stability due to increased mate- 
rial strength are sacrificed to the increased permeability 
and throughflow (11, p. 32). 

Other points of consideration include- 

1. The experiments moved quite quickly from the basic 
concepts of the first series of runs (Cambridge, 1977) to 
problems of considerable scientific depth. This necessi- 
tated using more sophisticated theoretical research design 
and running of the experiments. Particular reference is to 
the problems of seepage, erosion, and compactness. 

2. Throughout all three reports on the two Cambridge 
experiments (10-11, 40), the authors present, on a model 
by model basis, interesting scenarios as to an analogous 
prototype situation. A word of caution-these portrayals 
should not be taken too literally, for there is not enough 
experimental replication to ascertain their results. 



11 



Major problems encountered in this experiment were as 
follows: 

1. Questions exist involving capillary tension in slope 
stability and scaling the capillary tension to the prototype. 
These considerations were primarily due to the necessary 
reduction of particle size for modeling. 



2. Of most importance was the incompatibility of mod- 
eling permeability (which model proportional to D 10 / J~N 
grain size) and resistance to erosion (which model propor- 
tional to D 50 / N grain size) simultaneously. 

3. The compaction result is counter to the usual think- 
ing of the mining industry and certainly warrants more 
through investigation. 9 



FIRST EXPERIMENTAL SERIES-SANDIA NATIONAL LABORATORIES-1981 



EXPERIMENTAL GOAL AND DESIGN 

In 1980, Sandia National Laboratories decided to ex- 
pand usage of their large centrifuge facility to accommo- 
date geotechnical applications. In accordance, the Bureau 
and Sandia signed a series of interagency agreements to 
provide continuation of the waste embankment design 



series of centrifuge tests. The researcher's tests were the 
initial runs of this kind on Sandia's 25-ft centrifuge, in a 
sense, they were starting anew, and an orientation series of 
experiments seemed to be appropriate. 

9 Soil engineers have long recognized the value of compacting soil to 
produce a strong, settlement-free, water-resistant mass. 




////////////# 1 1 1 1 » » ' ,U 




Figure 4.— Sandia National Laboratories' 25-ft radius centrifuge. 



12 



Thus, the goals of the series were defined as follows: 
"The objective of this test series was to investigate the 
development of the phreatic surface and the scaling rela- 
tions associated with it. To accomplish this objective, a 
"modeling-of-models" approach (i.e., variation of model 
scale) was used. A single prototype embankment was 
scaled at three levels (90, 125, and 150 g) with 3 different 
embankment configurations being tested at each of the lev- 
els. The embankment was designed to be stable for all 
cases. The results illustrated the scaling phenomenon 
associated with the phreatic surface (37, pp. 2-3)." 

TEST EQUIPMENT 

Sandia's machine, with the specimen box aboard, is 
shown in figure 4. This 25-ft-radius machine is capable of 
attaining 240 g with a payload of about 8 st (2,000 lb/st). 
When the geotechnical swing bucket configuration is used, 
the machine is capable of 150 g with a payload of 2 st. A 
specimen box, specially constructed for the geotechnical 
series of experiments, had dimensions of 2.7 ft high, 3.7 ft 
long, and 8 in deep. Provisions are made to accommodate 
up to 12 transducers for the Bureau experiments. A 
means was provided to attain necessary waterflow levels 
throughout the embankment. Three types of cameras 
were available: video, movie, and still. 

EXPERIMENTAL RESULTS 

Three model configurations were used. One configu- 
ration represented a full-size embankment, while in the 
other two configurations the upstream face was sliced off 
just behind the embankment's crest. This style of model 
configuration was also used at the University of Cam- 
bridge. The advantage of aborting the upstream face is 
that a physically larger embankment can then be con- 
structed. To achieve the modeling-of-models effect, three 
acceleration levels (90, 125, and 150 g) were run on each 
model. The models were scaled in accordance with a fixed 
prototype geometry. This can be visualized by considering 
model height-the prototype height was 75 ft, the 90-g 



model height was 10 in, the 120-g model height was 7.5 in, 
while the 150-g model height was 6 in. Other dimensions 
were adjusted in a similar fashion. The experimental 
design was such that if the modeling-of-models concept 
was valid, all three phreatic surfaces would ideally map 
onto themselves when related to the prototype. To mea- 
sure the height of the phreatic surface in the experimental 
runs, a transducer system was installed; unfortunately, this 
system did not function properly. Instead, the experi- 
mental data was obtained by taking manual readings from 
video pictures of the centrifuge runs. Minor adjustment in 
particle size was necessary to meet permeability goals. 
Although slope stability failure calculations were made 
and compared with the results of the preliminary runs, this 
series was not designed for slope failures. Extensive ana- 
lytic techniques were used in both of the Sandia series of 
experiments. Several slope stability prediction methods 
were employed, while the automatic dynamic incremental 
nonlinear analysis of temperatures (ADINAT) finite- 
element program was used to predict the expected phreatic 
surface. The coal waste used was from the same 
southwestern site used for the two Cambridge series. 
Sandia performed extensive material properties test both 
prior and post to the centrifuge runs. Figure 5 shows a 
typical Sandia constructed embankment prior to running, 
while figure 6 illustrates an embankment after the centri- 
fuge run is completed. 

These Sandia centrifuge tests produced three 
conclusions: 

1. The shape of the phreatic surface was not parabolic 
concave downward, as was predicted by the finite-element 
programs. 

2. While the 90- and 125-g models map rather nicely, 
the 150-g model did not congrue with the other two. In 
fact, the phreatic surface is appreciably higher in all cases 
for the 150-g runs. Figure 7 illustrates this phenomenon. 

3. Since all three model geometries performed in a 
similar manner, it is not necessary to have a full-scale 
model, allowing the experiments to expand the dimensions 
of the critical part of the embankment only. 



13 




Figure 5.-Sandia experiment-embankment prior to testing. 



14 




Figure 6— Sandia experiment— embankment after testing. 



. 30 




30 40 50 60 70 

HORIZONTAL DISTANCE, m 



1 00 



Figure 7— Sandia's first experimental series— steady-state phreatic surface at 90-g, 125-g, and 150-g scaling. 



15 



Other points of consideration include- 

1. The centrifuge modeling adversely affected the phre- 
atic surface. The phreatic surface in the model clearly 
rises as the gravity-loading increases beyond 100 g. Pos- 
sible causes for this discrepancy include water seepage 
around the embankment, high-velocity fields in the 
embankment, and a curved gravitational field. Until 
resolved, care should be taken when modeling above 100 g. 

2. The numerical and experimental phreatic surface 
results up to about 100-g loading compare quite favorably. 
At 90- to 100-g loadings, the centrifuge results on slope 
failures involving seepage flow should closely resemble 
failures in the prototype. 

3. The slope stability conclusions were consistent with 
that obtained previously at Cambridge. 



4. The Sandia authors are of the opinion that the pri- 
mary use of centrifuge modeling is as a complementary 
tool to analytic modeling of phenomena. 

Major problems encountered in this experiment were as 
follows: 

1. The divergence between the three acceleration 
levels' phreatic surface is, of course, of primary concern. 
Explanations other than those offered by the authors have 
been expressed since completion of this work. An 
alternate hypothesis is that migration of fines within the 
embankment is responsible for the phreatic modeling-of- 
models discrepancies. 

2. Inverted curvature of the phreatic surface, also 
present to some degree in the Cambridge work, is still 
troublesome (37, pp. 39-40). 



SECOND EXPERIMENTAL SERIES-SANDIA NATIONAL LABORATORIES-1983 



EXPERIMENTAL GOAL AND DESIGN 

The basic goal of this experiment was to "determine 
the influence of packing density and material gradation 
(by the addition of slurried fines from the washing plant) 
on the embankment's stability" (38, p. 4). These concepts 
were suggested to the Bureau by Mining Health and 
Safety Administration (MSHA) as being practical field 
considerations. 

In this series of tests, slope stability is used as a mea- 
sure of success. The eight embankments models tested 
were all constructed marginally stable; thus, the introduc- 
tion of waterflow would then drive the embankment close 
to failure. The material was again taken from the same 
southwest mine as in the previously mentioned tests. 
Unfortunately, the material was quite different from previ- 
ous batches. It was quite "slakey" 10 in content which pro- 
vided the experimenter with many undesirable problems. 
The logistics of the situation was such that it was not pos- 
sible to start over with new material. Four different grada- 
tions of the material were used in this test series. 

TEST EQUIPMENT 

The basic experimental setup was the same as in the 
previous Sandia experiment. The transducers used to 



measure head pressure were operative and provided the 
basic data set for analysis. Video and still photography 
were also used to document the experiments. 

EXPERIMENTAL RESULTS 

As before, the finite-element code ADINAT was used 
for predicting the phreatic surface, while a computer pro- 
gram using the modified Bishop method of slices was used 
for slope stability analysis. In order to best display the 
transient waterflow through the embankment, equipotential 
contours of total head are used throughout the Sandia 
report (38). See figure 8 for typical test results. In this 
series of tests, the centrifuge was accelerated to 100 g and 
held there for the duration of the test. Slope stability pre- 
dictions are again consistent with the test results. The first 
two tests were run for calibration purposes, so there were 
six actual experimental tests of interest. As predicted by 
the slope stability computations, four of these failed, one 
of which failed due to piping. 11 A typical failed embank- 
ment is shown in figure 6. 

Of most interest were the two embankments that did 
not fail. In the first case the objective was to significantly 
increase the compaction state of the embankment. Having 
done this, this embankment was stable for the 34.7 time- 
equivalent days (a 5-min real-time centrifuge run) that it 



Slaking refers to the disintegration or loss of physical integrity of 
the material when re-wetted after drying. 



n Piping means that failure is induced on the downstream slope due 
to severe internal erosion. 



16 



2 1.7m 




18.5 12.011.5 8.7 

A- Test 1 , phreatic surface contours 




12.2 12.0 9.0 

B-Test 2, phreatic surface contours 

KEY 

▼ Phreatic surface 
33.4 m height 

Photographic 

Inferred from 

pressure data 




7 . 3 



6.0 6.2 4.4 



C-Test 6, illustrates difference between 
photographic and pressure transducer results 

Figure 8.— Sandia's second experimental series— equipotential contours. 



was run. The second embankment that did not fail was 
also heavily compacted. In addition, the reservoir was 
filled with slurried fines from the washing plant rather than 
with pea gravel. The water was introduced into the reser- 
voir only at the top of the fine-filled reservoir. This em- 
bankment was stable for the 69 time-equivalent days that 
it was run. 

There were some experimental difficulties which should 
be noted (38, pp. 34-35). To quote the authors: "The 



accumulated evidence from the entire series of tests iden- 
tified the photographic measurements of the phreatic sur- 
face as questionable." The primary explanation offered 
for this situation suggests that the embankment material 
may adhere to the surface of the viewing plate. Other 
possibilities for these major and local perturbations are 
presented. The authors feel that the transducers present 
more reliable information, because the transducer readings 
are more consistent with the theoretical calculations. 



17 



Figure 8C illustrates the discrepancies between the trans- 
ducer readings and the photographic results. 

A final note as to the philosophy of the Sandia experi- 
menters. They felt that a positive use of centrifuge 
modeling is the verification of computer modeling 
programs which predict slope stability and waterflow 
through the embankment (38, pp. 10-11). Therefore, 
computer modeling essentially represents the prototype in 
the Sandia experiments. This posture stands in strong 
contrast with the earlier soils centrifuge work of the 
Soviets (19, 26-29). The Soviets were concerned with 
directly designing a prototype embankment using the 
centrifuge as the analytic design tool. 

Major conclusions from this experiment were as follows: 

1. This test series again confirms the reliability of slope 
stability calculations. Generally speaking, failure occurs 



as predicted, but the physical failure pattern does not nec- 
essarily follow the assumed classical slip circle shape, as 
witnessed by the failure shown in figure 6. 

2. Several improvements are required for future exper- 
imental technique. In particular, the surface that mates 
the embankment to the viewplate must be disturbed as lit- 
tle as possible, and a construction technique must be 
developed to restrict the flow along this surface. 

3. For the material investigated, an increase in packing 
density can increase the stability of the embankment. The 
effects of gradation are more complicated. Although in- 
creasing the amount of fines in the reservoir increased the 
stability of the structure, these same fines restrict the flow 
of water through the embankment, thus limiting the dis- 
charge from the reservoir. Obviously, this presents other 
problems, e.g., increasing the probability of overtopping 
the reservoir. A similar problem exists for putting fines in 
the slurry behind the embankment. 



OTHER BUREAU OF MINES PROJECTS 



In addition to the four major centrifuge simulation test 
series, the following work has also been sponsored by the 
Bureau. 

GRAIN-SIZE MAPPING BETWEEN PROTOTYPES 
AND CENTRIFUGE MODELS 

As a result of conducting the four centrifuge test series, 
several problems evolved. One of the more interesting 
can be stated as follows: it is all well and good that the 
geometric dimensions scale between a model and its proto- 
type. Thus, a 1-ft-high centrifuge model may indeed rep- 
resent a 100-ft-high prototype. It is convenient that the 
same material may be used in model and prototype. This 
preserves many desirable features especially for estab- 
lishing similitude between the model and prototype. The 
question is whether one should also scale the grain-size 
distribution, for if one does not, is there not an imbalance? 
For example, wouldn't a grain of sand in a centrifuge 
model map into a boulder in the corresponding prototype? 

In collaboration with Deborah Goodings (Associate 
Professor of Civil Engineering, University of Maryland), 
the preceding problem was formulated as follows: investi- 
gate the influence of particle size relative to geotechnical 
centrifuge modeling. A most desirable feature of centri- 
fuge modeling is the use of prototype soil in the centrifuge 
test. As stated previously, the scientist strives for compli- 
ance with the laws of similitude whenever possible. The 
question is: should the soil's grain size also be scaled for 
similitude? Such scaling presents problems because scaling 
means that one is no longer working with the true proto- 
type soil. Thus, important inherent characteristics of the 
soil would necessarily be changed. 

It is not surprising that this question has been deemed 
important by many centrifuge users. Several publications 
were critiqued in which experiments discussed the effects 



of grain-size distribution on particular centrifuge modeling 
problems. Consensus seems to be that finely grained soils 
can be viewed as reacting as a continuum, thus there is no 
reason for grain-size scaling. However, coarser materials 
present more difficult problems. Some investigators have 
established workable bounds for making decisions on scal- 
ing grain size. Overson (20) concludes that there is no 
scale effect in modeling piling footings when the ratio of 
model diameter to average grain size lies between 30 and 
180. Other experimental rules exist for a variety of mod- 
eling situations. It is apparent that the grain-size ques- 
tion is an ongoing unresolved problem for centrifuge 
experiments. 

CENTRIFUGE USAGE TO SOLVE 
ROCK MECHANICS PROBLEMS 

Rock mechanics problems are certainly of prime inter- 
est to Bureau Research Centers. There are many unre- 
solved problems in theoretical rock mechanics that require 
solutions. For example, a classic dilemma is the incompat- 
ibility between physical properties measured in the labo- 
ratory and measured in situ. As outlined previously in the 
section on Rock Mechanics Centrifuge Testing, there have 
been several projects in which experiments used centri- 
fuges to explore rock mechanics problems. However, the 
number of rock mechanics centrifuge studies are certainly 
far less than that in soils. This is not surprising, for the 
problems in using a centrifuge for investigating rock 
mechanics theory are formidable. The most obvious stum- 
bling block is the strength of the rock. To do destructive 
testing of any kind, a large centrifuge capable of attaining 
2,000 g carrying a payload of several short tons is recom- 
mended. Such a machine does not exist today in the West- 
ern world. 



18 



For the preceding reasons, the Bureau decided to work 
in conjunction with Bill Pariseau, professor of mining 
engineering, University of Utah, Salt Lake City, UT. The 
goal of this effort was to investigate usage of a centrifuge 
to enhance rock mechanics theory. A first point of 
consideration is that 1-g models- prevalent in Europe and 
Australia, but not used in the United States-often require 
modification of materials to meet the scaling law 
requirements. Further, to simulate the underground 
environment properly, a model of 10 ft in height is in 
order. The cost of building such a model, plus that of 
constructing the necessary test frame, is deemed virtually 
prohibitive. The lack of such a facility explains to some 
degree the heavy reliance of researchers on theoretical 
calculations in rock mechanics. 

In spite of the difficulties, there are two theoretical rock 
mechanics problems that could be amenable to centrifuge 
solutions. The strength of centrifuge testing is highlighted 



when gravity stresses are roughly equivalent to the stresses 
of the material being tested. This is why, in soil mechan- 
ics, where the strength of sand and soils meet this requi- 
site, centrifuge testing is much simpler. In mining, one can 
also match this condition when addressing problems such 
as the flow of rock rubble, broken ore, and waste rock. 
Block cave mining is predicted on breaking the rock and 
then allowing gravity flow to move the rock to the miner's 
advantage. Thus, interesting problems of this kind could 
be simulated by centrifuge experimentation. 

Another centrifuge test series would aid in under- 
standing the role of joint continuity and spacing in caving 
mechanics in particular and rock mass mechanics in gen- 
eral. The basic idea is to fabricate a jointed roof and then 
increase the mine width until failure occurs, thus establish- 
ing a relationship between jointing and mining opening 
width. Both of the ideas discussed could be investigated 
with the centrifuges currently available. 



CONCLUSIONS 



The Bureau's sponsorship of large-scale centrifuge 
research has played an important role in the current 
renaissance of centrifuge applications in the geotechnical 
sciences in this country. Advantages and disadvantages of 
centrifuge modeling include- 

1. Capitalizing on the theoretical advantage of centri- 
fuge modeling-the exact mapping of stress and strain 
between the centrifuge model and the prototype-has been 
reasonably substantiated by these two test series. Use of 
the actual material of the embankment provides a realistic 
basis for modeling. 

2. All four test series showed a consistency between 
slope stability predictions of failure and actual model fail- 
ure. The Cambridge test series often produced the classi- 
cal failure slip surface. 

3. Although the theoretical laws of similitude are quite 
favorable for centrifuge modeling, in practice, many of the 
pertinent variables provide provocating results. Of par- 
ticular concern is the inability to model combinations of 
variables, such as erosion and mass instability. To truly 
simulate a prototype embankment, modeling should 
account for the interactions between the variables of 
concern. 

4. A positive result of centrifuge testing is the ability to 
simulate a variety of situations in a short time span. Con- 
struction of a model in a few hours is ideal for experi- 
ments that require destructive testing. However, centrifuge 
research and testing is very expensive and primarily con- 
fined to research environments. For the present, it is hard 



to envision the mining industry routinely using centrifuge 
modeling of tailings embankments as a practical design 
tool. 

In fairness to the potential of centrifuge testing in geo- 
technical work, the above conclusions certainly are not the 
final word on the subject. The four test series conducted 
at Cambridge and Sandia represent just a beginning in 
analyzing the advantage of centrifuge modeling. 
Unfortunately, the coal waste used provided varying de- 
grees of difficulty for the experimenters. Waste from 
metal mines may be a more fair material of consideration. 
In regard to tailings embankments, it is felt the classical 
slope stability problem has been sufficiently considered by 
both the Bureau's work and the work of others. 

Recommendations for future centrifuge testing of tail- 
ings embankments include- 

1. Better resolution of the compaction-erosion problem 
discussed in the second Cambridge experiment (72). 

2. Horizontal drain design theory of embankments has 
been a topic of interest for the Bureau (39). Computer 
program output for analytical calculations (41-42) could be 
compared with centrifuge modeling results. 

In addition, rock mechanics work would, of course, also 
be exciting and potentially rewarding to the mining indus- 
try and the rock mechanics community. Present accelera- 
tion limits on large-scale centrifuge in the United States 
provide a constraint to doing rock mechanics work. 



19 



REFERENCES 



1. Al-Hussaini, M. M. Centrifuge Model Testing of Soils: A 
Literature Review. U.S. Army Waterways Exp. Sta., Vicksburg, MS, 
Misc. Paper S-79-9, 1975, 35 pp. 

2. Bloomquist, D. G., and F. C. Townsend. Centrifugal Modeling 
of Phosphatic Clay Consolidation. Ch. in Sedimentation Consolidation 
Models; Predictions and Validation, ed. by R N. Young and F. C. 
Townsend. ASCE, 1984, pp. 565-580. 

3. Bucky, P. B. Use of Models for the Study of Mining Problems. 
AIME Tech. Publ. 425, Feb. 1931, pp. 3-28. 

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